Name: Discrete Mathematical Structures
ISBN: 9780132078457

arisbe__Jan 2022

First Khan Academy, then if you want to go further:

Bill Shillito | Introduction to Higher Mathematics (YouTube lecture course) - https://www.youtube.com/playlist?list=PLZzHxk_TPOStgPtqRZ6Kz...

Richard Hammack | Book of Proof (pdf book) - https://www.people.vcu.edu/~rhammack/BookOfProof/

Taylor Dupuy | Fundamentals of Mathematics (YouTube lecture course) - https://www.youtube.com/playlist?list=PLJmfLfPx1OedcIUn5nSCZ...

Silvanus P Thompson | Calculus Made Easy (html book) - https://calculusmadeeasy.org/ (This shouldn't be your only exposure to Calculus. It is more for building intuition.)

Dana Mosely | Understanding Basic Statistics (YouTube lecture course, no calculus) - https://www.youtube.com/playlist?list=PL9Wxhr5qVFN0WY2CXB4tR...

Gilbert Strang | Highlights of Calculus (YouTube lecture course) - https://www.youtube.com/playlist?list=PLBE9407EA64E2C318

Josh Starmer | StatQuest (Short various statistics videos) - https://www.youtube.com/c/joshstarmer/playlists

Bob Franzosa | Introduction to Topology (single public lecture) - https://www.youtube.com/watch?v=zsN_guq__Ac

Socratica | Abstract Algebra (short videos) - https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR...

MIT Calculus Revisited (Single Variable Calculus): https://www.youtube.com/playlist?list=PL3B08AE665AB9002A

MIT Calculus Revisited (Multivariable Calculus): https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B

MIT Calculus Revisited (Complex Variables, Differential Equations, Linear Algebra): https://www.youtube.com/playlist?list=PLD971E94905A70448

Matthew Macauley | Visual Group Theory, Differential Equations, Discrete Mathematical Structures, Advanced Linear Algebra, and Advanced Engineering Mathematics (YouTube lecture courses) - https://www.youtube.com/channel/UCH1cV4RtgI_N97M8jepiUzw/pla...

The Discrete Mathematics course above is probably the most important for your work. In fact I would look for more Discrete Mathematics courses if I were you as it is far more important than anything else here.

Open University (BBC) | Geometric Topology (YouTube lecture course) - https://www.youtube.com/playlist?list=PLKB3Q5Oyy_RNBrS3V2WbO...

Joel David Hamkins | Philosophy of Mathematics (YouTube lecture course) - https://www.youtube.com/playlist?list=PLg5tKDNI_a86OO6J9HuIn...

Marco Taboga | Probability and Statistics & Matrix Algebra (html book, need calculus) - https://www.statlect.com/

On YouTube you can literally watch a good lecture course for just about any typical undergraduate course. You just need to know where to look. Also there are even some really good master's degree courses out there.

Of course the only way to really learn the mathematics deeply is to "learn by doing", aka problems and proofs.

Other than the usual big American universities another good source from India is NPTEL (https://nptel.ac.in/course.html).

For somewhat more entertaining short lectures try:

Grant Sanderson | 3Blue1Brown - https://www.youtube.com/c/3blue1brown

Brady Haran | Numberphile - https://www.youtube.com/c/numberphile/

Tai-Danae Bradley, Gabe Perez-Giz, and Kelsey Houston-Edwards | PBS Infinite Series - https://www.youtube.com/c/pbsinfiniteseries/

Raymond Flood (YouTube public lectures at Gresham College) | History of Mathematics - https://www.youtube.com/playlist?list=PL_jwwOG0kPgPPiX0pcbzL...

There are a ton of channels starting to pop up like Grant's 3B1B (I find like a new one every week). He had a contest recently so maybe look at some of the winners.

Lastly this is pretty useful if you get into higher mathematics:

Math Vault | The Definitive Glossary of Higher Mathematical Jargon - https://mathvault.ca/math-glossary/

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dwdNov 2018

Nice choice.

I would add: An Introduction to Database Systems - Date

Also a few unmentioned so far: Discrete Mathematical Structures - Kolman

Introduction To Systems Analysis And Design - Hawryszkiewycz

Modern Operating Systems - Tanenbaum

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arisbe__May 2023

Bill Shillito | Introduction to Higher Mathematics (YouTube lecture course)

Richard Hammack | Book of Proof (pdf book) - https://www.people.vcu.edu/~rhammack/BookOfProof/

Short book: Groups and their Graphs

Taylor Dupuy | Fundamentals of Mathematics (YouTube lecture course)

Silvanus P Thompson | Calculus Made Easy (html book) - https://calculusmadeeasy.org/ (This shouldn't be your only exposure to Calculus. It is more for building intuition.)

Gilbert Strang | Highlights of Calculus (YouTube lecture course)

Josh Starmer | StatQuest (Short various statistics videos) - https://www.youtube.com/c/joshstarmer/playlists

Bob Franzosa | Introduction to Topology (single public lecture) - https://www.youtube.com/watch?v=zsN_guq__Ac

Socratica | Abstract Algebra (short videos)

MIT Calculus Revisited (Single Variable Calculus): https://www.youtube.com/playlist?list=PL3B08AE665AB9002A

MIT Calculus Revisited (Multivariable Calculus): https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B

MIT Calculus Revisited (Complex Variables, Differential Equations, Linear Algebra): https://www.youtube.com/playlist?list=PLD971E94905A70448

Matthew Macauley | Visual Group Theory, Differential Equations, Discrete Mathematical Structures, Advanced Linear Algebra, and Advanced Engineering Mathematics (YouTube lecture courses)

Open University (BBC) | Geometric Topology (YouTube lecture course)

Joel David Hamkins | Philosophy of Mathematics (YouTube lecture course)

Marco Taboga | Probability and Statistics & Matrix Algebra (html book, need calculus) - https://www.statlect.com/

On YouTube you can literally watch a good lecture course for just about any typical undergraduate course. You just need to know where to look. Also there are even some really good master's degree courses out there.

Of course the only way to really learn the mathematics deeply is to "learn by doing", aka problems and proofs.

Other than the usual big American universities another good source from India is NPTEL (https://nptel.ac.in/course.html).

For somewhat more entertaining short lectures try:

Grant Sanderson | 3Blue1Brown - https://www.youtube.com/c/3blue1brown

Brady Haran | Numberphile - https://www.youtube.com/c/numberphile/

Tai-Danae Bradley, Gabe Perez-Giz, and Kelsey Houston-Edwards | PBS Infinite Series - https://www.youtube.com/c/pbsinfiniteseries/

Raymond Flood (YouTube public lectures at Gresham College) | History of Mathematics

There are a ton of channels starting to pop up like Grant's 3B1B (I find like a new one every week). He had a contest recently so maybe look at some of the winners.

This is pretty useful if you get into higher mathematics:

Math Vault | The Definitive Glossary of Higher Mathematical Jargon - https://mathvault.ca/math-glossary/

Some books:

There is Eugenia Cheng's book: The Joy of Abstraction

See this list its pretty good: https://abakcus.com/30-best-math-books-to-learn-advanced-mat...

P.S. I created some Youtube lecture aggregation channels:

https://arisbe.carrd.co/#section03

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lkbmOct 2020

One amusing thing I saw in the two courses I mentioned is that in Intro to Logic, we spent something like a month learning each of the eighteen rules of inference, gradually adding a couple each day until we were familiar with all of them.

In Discrete Math, the professor wrote out the eighteen rules in as part of a single lecture and then we had homework due that same week wherein we were expected to know and use all of them. (He may have introduced predicate logic in that same lecture.)

Intro to Logic was a philosophy course, but some majors allowed students to take it instead of their one required College Algebra course. The result was it was a lot of very non-technical people who struggled with intro algebra, and consequently struggled with formal logic. (Predicate logic was the focus of the third section of the course later on.)

Discrete Mathematical Structures was a math/cs course, where almost every student was a CS major, so it was predominantly technically-minded people for whom formal logic was at least very familiar, if not natural.

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